NEW SOUND EFFECTS FOR GAME.

Sample packs are generally not that expensive compared to an instrument/library for music production. Libraries are usually in the $100-$200 range for a good virtual instrument or SFX package, but you can tweak them and customize the sound since under the hood of the library there would be a gigabyte of samples that the code uses to glue together into a good sound. Typically they are also not standalone programs and only work in something that accepts vst plugins. However, while $30-$50 may be a reasonable price (depending on how much you're actually getting), what you're looking at seems to be geared towards either music production, or movie soundtrack usage, and not for games.

For non-commercial use, freesound.org is a good internet search engine for sound effects, but it doesn't guarantee that the sounds are really public to use.

For possibly commercial use, there are a few options available. If the sounds you need are 8-bit-ish, you can download SFXR (free, just search for it) which is a fast customized program to make various 8bit-like sounds, primarily designed for game jams. For something a bit more complicated, like 16-bit era sound effects, you can use a program like Audacity (also free, just search for it), you can download a reference sound (eg: ffvi's door open sound), and then zoom down into the sample level to see how the sound changes over time and then, by hand, draw out a similar waveform on a new track. It won't sound the same, but it'll sound fairly similar, and you can use the effects in Audacity (speed change, pitch change, etc.) to tweak the sound a bit.

Finally, there's always Foley, which is the traditional art of recording sounds for movies. Again, using Audacity (it's a great free program), you can use your mic to record various sounds (crunching lettuce, splashing water, etc.), and you can search online for ideas of how to Foley something (my favorite is working up some phlegm to make monster sounds and then doing pitch/speed changes to them). The main thing to be careful of here is to make sure you're not recording echo, since that's really, really hard to remove from the sample, and preferably use an external mic instead of a laptop mic. Laptop mics usually pick up the fan/hard drive sound of the laptop and it's harder to get rid of. Even with a really crappy mic, you can get good sound effects by using the noise reduction in Audacity (select a section of the sample where the sound is not playing, and it'll use the background noise in that section to remove from the parts with sound). You get a bit of artifacts from the noise reduction, but they're always way quieter than the noise was.

You might also be find sample packs geared towards games in other places. There's a few listed on this site in the resources section I believe.